The relation between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime

The connection between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime is studied. We derive a new relationship between these correlation functions under the scaling hypothesis. In particular, we find that the three-point correlation function, ζ , obeys the scaling law, ζ ∝ ξ 3m+4w 2m+2w , once the Fourier phases remain correlated due to non-linear gravitational clustering, where ξ, m, and w are the two-point correlation function, the power index of the power spectrum in the non-linear regime, and the number of the spatial dimension, respectively. That is, the power index of the three-point correlation function depends only on the two-point correlation, and deviates from that of “hierarchical form”, ζ ∝ ξ, generally. Furthermore, our numerical results in the one-dimensional Einstein-de Sitter model support our analytical expression rather than the “hierarchical form”. Subject headings: cosmology: theory – large-scale structure of universe – methods: – analytical – methods: – numerical – methods: statistical